Socklisten on an obscure port and only give out your IP (which would be your URL) along with the port to those you trust. On mIRC create a socket script to accept connections and, if you send the necessary header, you can have a web server set up on mIRC. You can generate the HTML when a certain page is requested, /bread it from the file then sockwrite the binary var then close the connection after it has been written. If you want to know the commands that are sent from a server to a browser connect to any website on mIRC using /server on port 80 and look at the debug window.
You could also alternatively download a web server for mIRC at
www.mircscripts.org but making it can be fun and interesting too